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CS4335 Design and Analysis of Algorithms
Tutorial Two
Exercise 1. Use the learned algorithm to produce an Euler circuit for the following
graph. (Moderate Part)
Exercise 2. Show that the following statement is NOT correct.
Statement: If the degree of every vertex in a graph is even, then there exists a Hamilton
circuit for the graph.
If you have extra time, think about the following question.
Question: In a map, two countries are neighbors if they share a common border. Given
a map, we want to know if it is possible to find a tour starting from a country, going
across each border once and come back to the starting country.
For example, the following is a map containing 8 countries A, B, … H. Does there exist
such a tour for this map? Give an algorithm to solve the problem. Here we assume that
two countries can share only one segment of border. (What if two countries may share
more than one segment of border? ) (Hint: Construct a new graph ….)
A
C
B
F
D
E
H
G